Reversing and non-reversing Taylor vortex flows in modulated Taylor–Couette flow with counter-oscillating cylinders

Abstract

Two classes of time-periodic Taylor vortex flows, called reversing and non-reversing flows, were discovered by Youd et al. (2003) under the effect of a zero mean inner cylinder’s angular velocity modulation with fixed outer cylinder. In the non-reversing/reversing flow, which takes place at relatively high/low frequency, the direction of the Taylor vortices in the radial axial-plane is conserved/ not conserved and does not change/change every half-cycle/cycle. This dynamic has been explained on the basis of the time period (frequency) provided by the driving force whether it is sufficiently enough for such flow reversal to be produced. In this paper, we show, using Floquet theory, that the counter-oscillation of the outer cylinder leads to a non-reversing flow suppression in some frequency ranges. In this case, this latter type of Taylor vortex flow could occur only in the very high frequency limit. Taking into account existing results concerning the case of co-oscillating cylinders, it is concluded that the mechanism governing the apparition of such flow reversal in the system does not depends solely to the oscillation frequency but strongly depends on the oscillation of the outer cylinder also.On the other hand, the reported numerical stability diagrams related to this flow configuration (counter-oscillating cylinders) reproduce quite well the existing experimental findings carried-out by Tennakoon et al. (1997). Explanation of discontinuities and jumps pointed-out by these authors in their numerical and experimental stability diagrams is also presented in the framework of the present investigation where we show that these phenomena are due to a switch in the instability of the system between the reversing and non-reversing flows.